Closed-Form Sum-Rate Analysis of Interference Alignment with Limited Feedback Based on Scalar Quantization and Random Vector Quantization

Interference alignment (IA) is a promising interference management technique to achieve the theoretical optimal degree of freedom (DoF) performance in multi-user cooperation scenarios. However, the effective achievable sum-rate performance of IA is largely affected by the feedback overhead and accuracy of channel state information (CSI) and decoding information (DI). Therefore, it is critical to establish the exact relationship between feedback overhead and the achievable sum-rate of IA to obtain the optimal effective performance. Most existing IA performance analysis approaches focus on the vector quantization (VQ)-based feedback strategy, but the implementation complexity of VQ will be excessive when more quantization bits are required to achieve the expected quantization accuracy for larger-sized matrices or higher signal-to-noise ratio (SNR) regimes. Moreover, the obtained achievable sum-rate formulas are too complicated for quick performance evaluation. In this paper, a new sum-rate performance analysis method for IA under different quantization and feedback strategies is proposed to achieve a trade-off between accuracy and complexity, and the closed-form achievable sum-rate expressions are derived. First, in the IA case with random vector quantization (RVQ)-based CSI feedback, the quantization error of RVQ is transformed into the equivalent VQ error of the Gaussian channel error, based on which the achievable sum-rate formula is obtained. Second, in the IA case with scalar quantization (SQ)-based CSI feedback, the relationship between the effective sum-rate and SQ bits is established. Third, in the IA case with SQ-based CSI feedback and RVQ-based DI feedback, the achievable sum-rate formula is derived by combining these two kinds of quantization errors. Finally, the simulation results confirm that the theoretical results are accurate enough, which can help to determine the optimal CSI feedback overhead in practical channel conditions. Moreover, the theoretical and simulation results demonstrate that RVQ may be more applicable to IA scenarios with fewer receiving antennas and low SNR regimes.